Problem 3. (5 pts) A new diet is tested. The data below show the result on 36 pa
ID: 3182046 • Letter: P
Question
Problem 3. (5 pts) A new diet is tested. The data below show the result on 36 patients. Make a decision whether the new diet is working with confidence 99%. MUST USE CONFIDENCE INTERVALS.
PATIENT NO.
WEIGHT BEFORE
WEIGH AFTER
1
282
280
2
289
281
3
309
294
4
286
265
5
310
295
6
343
343
7
330
322
8
343
335
9
288
282
10
313
295
11
290
274
12
320
328
13
301
290
14
345
339
15
299
271
16
339
320
17
339
320
18
350
321
19
337
319
20
336
338
21
312
285
22
332
340
23
338
314
24
317
300
25
310
310
26
311
292
27
320
328
28
282
288
29
336
322
30
306
284
31
282
280
32
289
281
33
309
294
34
286
265
35
310
295
36
343
343
PATIENT NO.
WEIGHT BEFORE
WEIGH AFTER
1
282
280
2
289
281
3
309
294
4
286
265
5
310
295
6
343
343
7
330
322
8
343
335
9
288
282
10
313
295
11
290
274
12
320
328
13
301
290
14
345
339
15
299
271
16
339
320
17
339
320
18
350
321
19
337
319
20
336
338
21
312
285
22
332
340
23
338
314
24
317
300
25
310
310
26
311
292
27
320
328
28
282
288
29
336
322
30
306
284
31
282
280
32
289
281
33
309
294
34
286
265
35
310
295
36
343
343
Explanation / Answer
The weight decrease after the diet taken for 36 patients are
2 8 15 21 15 0 8 8 6 18 16 -8 11 6 28 19 19 29 18 -2 27 -8 24 17 0 19 -8 -6 14 22 2 8 15 21 15 0
Null Hypothesis H0: The diet is not working and the weight decrease = 0
Alternative Hypothesis H1: The diet is working and the weight decrease > 0
The mean decrease in weight = 11.08
The standard deviation of decrease in weight = 10.6
The standard error of the mean is = 10.6/sqrt(36) = 10.6/6 = 1.76
z-value = (mean weight - hypothesized value)/ standard error
= (11.08 - 0 )/ 1.76 = 6.295
Using, z-table chart, z-value at 99% confidence interval is 2.326.
As calculated, z-value 6.295 > z-value at 99% confidence interval (2.326), we reject the null hypothesis and accept the alernative hypothesis that there is decrease in weight and new diet is working.
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